(i) The term proportional to \(\sin k\)  produces the cross hopping, where
\(\sin k=(e^{ik}-e^{-ik})/2i\)  represents an imaginary hopping in the
tight-bind model. The imaginary hopping is implemented by a negative
impedance converter \(R_{X}\)  with current inversion[1]}, as is
constructed based on an operational amplifier with resistors: See Fig.REF (b).
The voltage-current relation is given by
\(\left(\begin{array}{c}I_{1} \\I_{2}\end{array}\right) =\frac{1}{R_{X}}\left(\begin{array}{cc}-\nu & \nu \\-1 & 1\end{array}\right) \left(\begin{array}{c}V_{1} \\V_{2}\end{array}\right) ,\) 
